L2DensityGoFtest (version 0.6.0)

kde: Kernel Density Estimation

Description

Implements the (classical) kernel density estimator, see (2.2a) in Silverman (1986).

Usage

kde(xin, xout, h, kfun)

Value

A vector with the density estimates at the designated points xout.

Arguments

xin

A vector of data points. Missing values not allowed.

xout

A vector of grid points at which the estimate will be calculated.

h

A scalar, the bandwidth to use in the estimate, e.g. bw.nrd(xin)

kfun

Kernel function to use. Supported kernels: Epanechnikov, Biweight, Gaussian, Rectangular, Triangular.

Author

R implementation and documentation: Dimitrios Bagkavos <[e-mail]>

Details

The classical kernel density estimator is given by $$\hat f(x;h) = n^{-1}\sum_{i=1}^n K_h(x-X_{i})$$ \(h\) is determined by a bandwidth selector such as Silverman's default plug-in rule.

References

Silverman (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.

Examples

x<-seq(-5, 5,length=100)          #design points where the estimate will be calculated
plot(x, dnorm(x),  type="l", xlab = "x", ylab="density") #plot true density function
SampleSize <- 100
ti<- rnorm(SampleSize)            #draw a random sample from the actual distribution

huse<-bw.nrd(ti)
arg2<-kde(ti, x, huse, Epanechnikov) #Calculate the estimate
lines(x, arg2, lty=2)             #draw the result on the graphics device.